A brief history of relativity

What is it? How does it work? Why does it change everything? An
easy primer by the world's most famous living physicist

By Stephen Hawking

December 27, 1999
Web posted at: 12:28 p.m. EST (1728 GMT)

Toward the end of the 19th century scientists believed they were
close to a complete description of the universe. They imagined
that space was filled everywhere by a continuous medium called
the ether. Light rays and radio signals were waves in this ether
just as sound is pressure waves in air. All that was needed to
complete the theory was careful measurements of the elastic
properties of the ether; once they had those nailed down,
everything else would fall into place.

Soon, however, discrepancies with the idea of an all-pervading
ether began to appear. You would expect light to travel at a
fixed speed through the ether. So if you were traveling in the
same direction as the light, you would expect that its speed
would appear to be lower, and if you were traveling in the
opposite direction to the light, that its speed would appear to
be higher. Yet a series of experiments failed to find any
evidence for differences in speed due to motion through the
ether.

The most careful and accurate of these experiments was carried
out by Albert Michelson and Edward Morley at the Case Institute
in Cleveland, Ohio, in 1887. They compared the speed of light in
two beams at right angles to each other. As the earth rotates on
its axis and orbits the sun, they reasoned, it will move through
the ether, and the speed of light in these two beams should
diverge. But Michelson and Morley found no daily or yearly
differences between the two beams of light. It was as if light
always traveled at the same speed relative to you, no matter how
you were moving.

The Irish physicist George FitzGerald and the Dutch physicist
Hendrik Lorentz were the first to suggest that bodies moving
through the ether would contract and that clocks would slow.
This shrinking and slowing would be such that everyone would
measure the same speed for light no matter how they were moving
with respect to the ether, which FitzGerald and Lorentz regarded
as a real substance.

But it was a young clerk named Albert Einstein, working in the
Swiss Patent Office in Bern, who cut through the ether and solved
the speed-of-light problem once and for all. In June 1905 he
wrote one of three papers that would establish him as one of the
world's leading scientists--and in the process start two
conceptual revolutions that changed our understanding of time,
space and reality.

In that 1905 paper, Einstein pointed out that because you could
not detect whether or not you were moving through the ether, the
whole notion of an ether was redundant. Instead, Einstein started
from the postulate that the laws of science should appear the
same to all freely moving observers. In particular, observers
should all measure the same speed for light, no matter how they
were moving.

This required abandoning the idea that there is a universal
quantity called time that all clocks measure. Instead, everyone
would have his own personal time. The clocks of two people would
agree if they were at rest with respect to each other but not if
they were moving. This has been confirmed by a number of
experiments, including one in which an extremely accurate
timepiece was flown around the world and then compared with one
that had stayed in place. If you wanted to live longer, you could
keep flying to the east so the speed of the plane added to the
earth's rotation. However, the tiny fraction of a second you
gained would be more than offset by eating airline meals.

Einstein's postulate that the laws of nature should appear the
same to all freely moving observers was the foundation of the
theory of relativity, so called because it implies that only
relative motion is important. Its beauty and simplicity were
convincing to many scientists and philosophers. But there
remained a lot of opposition. Einstein had overthrown two of the
Absolutes (with a capital A) of 19th century science: Absolute
Rest as represented by the ether, and Absolute or Universal Time
that all clocks would measure. Did this imply, people asked, that
there were no absolute moral standards, that everything was
relative?

This unease continued through the 1920s and '30s. When Einstein
was awarded the Nobel Prize in 1921, the citation was for
important--but by Einstein's standards comparatively minor--work
also carried out in 1905. There was no mention of relativity,
which was considered too controversial. I still get two or three
letters a week telling me Einstein was wrong. Nevertheless, the
theory of relativity is now completely accepted by the scientific
community, and its predictions have been verified in countless
applications.

A very important consequence of relativity is the relation
between mass and energy. Einstein's postulate that the speed of
light should appear the same to everyone implied that nothing
could be moving faster than light. What happens is that as energy
is used to accelerate a particle or a spaceship, the object's
mass increases, making it harder to accelerate any more. To
accelerate the particle to the speed of light is impossible
because it would take an infinite amount of energy. The
equivalence of mass and energy is summed up in Einstein's famous
equation E=mc2, probably the only physics equation to have
recognition on the street.

Among the consequences of this law is that if the nucleus of a
uranium atom fissions (splits) into two nuclei with slightly less
total mass, a tremendous amount of energy is released. In 1939,
with World War II looming, a group of scientists who realized the
implications of this persuaded Einstein to overcome his pacifist
scruples and write a letter to President Roosevelt urging the
U.S. to start a program of nuclear research. This led to the
Manhattan Project and the atom bomb that exploded over Hiroshima
in 1945. Some people blame the atom bomb on Einstein because he
discovered the relation between mass and energy. But that's like
blaming Newton for the gravity that causes airplanes to crash.
Einstein took no part in the Manhattan Project and was horrified
by the explosion.

Although the theory of relativity fit well with the laws that
govern electricity and magnetism, it wasn't compatible with
Newton's law of gravity. This law said that if you changed the
distribution of matter in one region of space, the change in the
gravitational field would be felt instantaneously everywhere else
in the universe. Not only would this mean you could send signals
faster than light (something that was forbidden by relativity),
but it also required the Absolute or Universal Time that
relativity had abolished in favor of personal or relativistic
time.

Einstein was aware of this difficulty in 1907, while he was still
at the patent office in Bern, but didn't begin to think seriously
about the problem until he was at the German University in Prague
in 1911. He realized that there is a close relationship between
acceleration and a gravitational field. Someone in a closed box
cannot tell whether he is sitting at rest in the earth's
gravitational field or being accelerated by a rocket in free
space. (This being before the age of Star Trek, Einstein thought
of people in elevators rather than spaceships. But you cannot
accelerate or fall freely very far in an elevator before disaster
strikes.)

If the earth were flat, one could equally well say that the apple
fell on Newton's head because of gravity or that Newton's head
hit the apple because he and the surface of the earth were
accelerating upward. This equivalence between acceleration and
gravity didn't seem to work for a round earth, however; people on
the other side of the world would have to be accelerating in the
opposite direction but staying at a constant distance from us.

On his return to Zurich in 1912 Einstein had a brainstorm. He
realized that the equivalence of gravity and acceleration could
work if there was some give-and-take in the geometry of reality.
What if space-time--an entity Einstein invented to incorporate the
three familiar dimensions of space with a fourth dimension,
time--was curved, and not flat, as had been assumed? His idea was
that mass and energy would warp space-time in some manner yet to
be determined. Objects like apples or planets would try to move
in straight lines through space-time, but their paths would
appear to be bent by a gravitational field because space-time is
curved.

With the help of his friend Marcel Grossmann, Einstein studied
the theory of curved spaces and surfaces that had been developed
by Bernhard Riemann as a piece of abstract mathematics, without
any thought that it would be relevant to the real world. In 1913,
Einstein and Grossmann wrote a paper in which they put forward
the idea that what we think of as gravitational forces are just
an expression of the fact that space-time is curved. However,
because of a mistake by Einstein (who was quite human and
fallible), they weren't able to find the equations that related
the curvature of space-time to the mass and energy in it.

Einstein continued to work on the problem in Berlin, undisturbed
by domestic matters and largely unaffected by the war, until he
finally found the right equations, in November 1915. Einstein
had discussed his ideas with the mathematician David Hilbert
during a visit to the University of Gottingen in the summer of
1915, and Hilbert independently found the same equations a few
days before Einstein. Nevertheless, as Hilbert admitted, the
credit for the new theory belonged to Einstein. It was his idea
to relate gravity to the warping of space-time. It is a tribute
to the civilized state of Germany in this period that such
scientific discussions and exchanges could go on undisturbed
even in wartime. What a contrast to 20 years later!

The new theory of curved space-time was called general relativity
to distinguish it from the original theory without gravity, which
was now known as special relativity. It was confirmed in
spectacular fashion in 1919, when a British expedition to West
Africa observed a slight shift in the position of stars near the
sun during an eclipse. Their light, as Einstein had predicted,
was bent as it passed the sun. Here was direct evidence that
space and time are warped, the greatest change in our perception
of the arena in which we live since Euclid wrote his Elements
about 300 B.C.

Einstein's general theory of relativity transformed space and
time from a passive background in which events take place to
active participants in the dynamics of the cosmos. This led to a
great problem that is still at the forefront of physics at the
end of the 20th century. The universe is full of matter, and
matter warps space-time so that bodies fall together. Einstein
found that his equations didn't have a solution that described a
universe that was unchanging in time. Rather than give up a
static and everlasting universe, which he and most other people
believed in at that time, he fudged the equations by adding a
term called the cosmological constant, which warped space-time
the other way so that bodies move apart. The repulsive effect of
the cosmological constant would balance the attractive effect of
matter and allow for a universe that lasts for all time.

This turned out to be one of the great missed opportunities of
theoretical physics. If Einstein had stuck with his original
equations, he could have predicted that the universe must be
either expanding or contracting. As it was, the possibility of a
time-dependent universe wasn't taken seriously until
observations were made in the 1920s with the 100-in. telescope
on Mount Wilson. These revealed that the farther other galaxies
are from us, the faster they are moving away. In other words,
the universe is expanding and the distance between any two
galaxies is steadily increasing with time. Einstein later called
the cosmological constant the greatest mistake of his life.

General relativity completely changed the discussion of the
origin and fate of the universe. A static universe could have
existed forever or could have been created in its present form at
some time in the past. On the other hand, if galaxies are moving
apart today, they must have been closer together in the past.
About 15 billion years ago, they would all have been on top of
one another and their density would have been infinite. According
to the general theory, this Big Bang was the beginning of the
universe and of time itself. So maybe Einstein deserves to be the
person of a longer period than just the past 100 years.

General relativity also predicts that time comes to a stop
inside black holes, regions of space-time that are so warped
that light cannot escape them. But both the beginning and the
end of time are places where the equations of general relativity
fall apart. Thus the theory cannot predict what should emerge
from the Big Bang. Some see this as an indication of God's
freedom to start the universe off any way God wanted. Others
(myself included) feel that the beginning of the universe should
be governed by the same laws that hold at all other times. We
have made some progress toward this goal, but we don't yet have
a complete understanding of the origin of the universe.

The reason general relativity broke down at the Big Bang was
that it was not compatible with quantum theory, the other great
conceptual revolution of the early 20th century. The first step
toward quantum theory came in 1900, when Max Planck, working in
Berlin, discovered that the radiation from a body that was
glowing red hot could be explained if light came only in packets
of a certain size, called quanta. It was as if radiation were
packaged like sugar; you cannot buy an arbitrary amount of loose
sugar in a supermarket but can only buy it in 1-lb. bags. In one
of his groundbreaking papers written in 1905, when he was still
at the patent office, Einstein showed that Planck's quantum
hypothesis could explain what is called the photoelectric
effect, the way certain metals give off electrons when light
falls on them. This is the basis of modern light detectors and
television cameras, and it was for this work that Einstein was
awarded the 1921 Nobel Prize in Physics.

Einstein continued to work on the quantum idea into the 1920s but
was deeply disturbed by the work of Werner Heisenberg in
Copenhagen, Paul Dirac in Cambridge and Erwin Schrodinger in
Zurich, who developed a new picture of reality called quantum
mechanics. No longer did tiny particles have a definite position
and speed. On the contrary, the more accurately you determined
the particle's position, the less accurately you could determine
its speed, and vice versa.

Einstein was horrified by this random, unpredictable element in
the basic laws and never fully accepted quantum mechanics. His
feelings were expressed in his famous God-does-not-play-dice
dictum. Most other scientists, however, accepted the validity of
the new quantum laws because they showed excellent agreement with
observations and because they seemed to explain a whole range of
previously unaccounted-for phenomena. They are the basis of
modern developments in chemistry, molecular biology and
electronics and the foundation of the technology that has
transformed the world in the past half-century.

When the Nazis came to power in Germany in 1933, Einstein left
the country and renounced his German citizenship. He spent the
last 22 years of his life at the Institute for Advanced Study in
Princeton, N.J. The Nazis launched a campaign against "Jewish
science" and the many German scientists who were Jews (their
exodus is part of the reason Germany was not able to build an
atom bomb). Einstein and relativity were principal targets for
this campaign. When told of publication of the book One Hundred
Authors Against Einstein, he replied, Why 100? If I were wrong,
one would have been enough.

After World War II, he urged the Allies to set up a world
government to control the atom bomb. He was offered the
presidency of the new state of Israel in 1952 but turned it
down. "Politics is for the moment," he once wrote, "while...an
equation is for eternity." The equations of general relativity
are his best epitaph and memorial. They should last as long as
the universe.

The world has changed far more in the past 100 years than in any
other century in history. The reason is not political or economic
but technological--technologies that flowed directly from advances
in basic science. Clearly, no scientist better represents those
advances than Albert Einstein: TIME's Person of the Century.

Professor Hawking, author of A Brief History of Time, occupies
the Cambridge mathematics chair once held by Isaac Newton